Final answer:
The function f(x)=-(x+4)^3 has a single real zero at x = -4 with multiplicity 3. The graph touches the x-axis and turns around at this point, resulting in exactly one real zero.
Step-by-step explanation:
The function given is f(x)=-(x+4)³. To find the real zeros and their multiplicities, we need to find the values of x that make the function equal to zero. In this case, the equation simplifies to (x+4)³ = 0. Solving for x, we get a single real zero at x = -4. Since the factor (x+4) is raised to the power of three, the multiplicity of this zero is 3, meaning that the graph of the function touches the x-axis and turns around at x = -4. The number of real zeros for this function is one.